Mechanical strength variability of deformed reinforcing steel bars for concrete structures in Ethiopia

The paper presents statistical analysis of mechanical strength and linear density properties of deformed reinforcing Grade 60 steel bars. Two different lots of samples are identified based on test years for the years 2015–2017 as Lot 1 and 2018–2020 as Lot 2. Yield strength (YS), tensile strength (TS), elongation, mass per length and characteristic ratio of TS and YS are analyzed for rebar diameters of 8, 10, 12 and 16 mm considering both lots. Mechanical and linear density properties are compared statistically using range, mean, standard deviation, coefficient of variance, skewness and kurtosis of the recorded sets of values. Moreover, the results of YS, TS and elongation are analyzed separately by one-way analysis of variance for both lots. The result shows that the aggregate mean values of YS, TS and elongation for Lot 1 and Lot 2 are 593.1 MPa, 701.1 MPa, 14.78%; and 572.5 MPa, 673.8 MPa, 15.47%, respectively. Even though there is a slight decrement in values of YS and TS and increment in elongation from Lot 1 to Lot 2, both lots exceeded values recommended by ASTM A615 standard. Furthermore, with 95% confidence interval, one-way analysis of variance showed that the aggregate data of rebars are dissimilar in terms of YS, TS and percentage elongation with figures showing decrement from Lot 1 to Lot 2.

www.nature.com/scientificreports/ Djavanroodi and Salman 6 analyzed statistical variability of mechanical properties and weight of grade 60 reinforcing steel bars. The study investigated 130 samples for yield strength, tensile strength and elongation. 60 bars were investigated for variability of weight.
Carrillo et al. 4 characterized stress-strain curves of steel reinforcing bars marketed in Bogota. 60 samples with diameters ranging from 9.5 mm to 25.5 mm were tested for tensile strength. The aggregate results were statistically analyzed and compared with other countries i.e. US, India and Mexico.
Tavio et al. 8 in addition to yield strength, tensile strength and elongation, investigated ratio of tensile to yield strength of various steel grades and bar sizes. The test results were analyzed and compared among steel grades and with ASTM, IS 22 , ACI 21 and Russian standards.
Rafi et al. 13 investigated the variability of chemical and mechanical properties of cold-twisted and hot-rolled ribbed reinforcement steel bars of diameters ranging from 10 to 40 mm. The result showed a large variation in reinforcement bar strength for which design implications were studied as failure mode of flexure members might exhibit a change from ductile to brittle.
Bournonville et al. 26 investigated statstical variability of mechanical properties of of reinforcement steel bars produced in the US and Canada. 100 samples were collected from 29 reinforcemnt steel manufacturing industries. The statistical report included parameters such as mean, median, standard deviation, cofficient of variance, skewness and kurtosis.
Alo et al. 27 reported statistical assessment of mechanical properties of locally produced and imported reinforced steels used in Nigeria. One-way ANOVA analysis was conducted to indicate the variability of the reinforcing bars in terms of yield strength, tensile strength and elongation.
Variability analysis of mechanical properties of reinforcement steel bars plays a great role in assessing homogeneity of steel products used in the construction projects. Hence, the purpose of this work is to statistically analyze mechanical and linear density properties of reinforcing bars that were used in Ethiopian construction industry between the years 2015 and 2020 and make comparison with standards.

Materials and methods
Types and sample size of reinforcing steel. Two groups of samples are formed based on test period, namely Lot 1 and Lot 2 for tests conducted in the years 2015-2017 and 2018-2020, respectively. Both lots are collected from Ethiopian market irrespective of their source i.e. locally produced or imported steel bars. The sampling is carried out by the contractors and supervisors working in their respective construction projects. Samples are Grade 60 steel that comprise of four different diameters that are highly utilized by Ethiopian construction market 1 .
The sample size of each diameters and lots are listed in Table 1.
Test specimen preparation. All specimens were cut into a total length of 400 mm for tensile testing. Means and standard deviations are computed using the following procedure. After the desired numbers of test have been conducted on a particular lot for a specific variable, the mean value of n number of intercepts has been calculated according to: where X i represents an individual value and n is the number of total tests.
(1) X = X i n For yield strength, tensile strength, elongation percentage and mass per length, the following parameters are evaluated for each bar size in each lot: mean, median, standard deviation, coefficient of variation, minimum, maximum, skewness, and kurtosis. The skewness is a measurement of data symmetry. Negative values show data that is skewed to the left while positive values indicate data that is skewed to the right. The kurtosis is a degree whether the data is peaky or flat relative to a normal distribution. An increased kurtosis indicates an increased peak near the mean of the data. Ranges are determined as minimum and maximum values from the total test conducted (Figs. 1,2,3,4,5,6,7,8). Summary statistics for bars of each size and lot are included in Tables 3, 4  One-way analysis of variance for one factor one level test type is designed by which YS, TS, EL and TS/YS for the aggregate in each lot are analyzed using ANOVA 1,28 as presented in Table 2.

Experimental results and discussion
This section discusses and summarizes the test results obtained in tensile test and linear density measurements (Tables 1, 2       The influence of yield strength (YS) on the TS/YS ratio is found to be as expected for Lot 1 and Lot 2. The ratio decreases with increasing the yield strength which in turn is expected to reduce the ductility of the materials at higher yield strength. The mean TS/YS ratio of Lot 1 and Lot 2 is 1.20 and 1.15, respectively, which is below ASTM requirement 25 . 68% of the samples in Lot 1 and 82% in Lot 2 fail to meet the ASTM requirement for TS/YS ratio.
The statistical analysis including the values of maximum, minimum, average, variance, coefficient of variance, standard deviation, skewness, and kurtosis for yield strength, tensile strength, elongation and mass per length are calculated. Tables 3, 4 and 6 summarize the statistical analysis of yield strength, tensile strength, elongation and mass per length for 8, 10, 12, and 16 mm diameter bars and aggregate result of the two lots. From the results of COV, it's noted that mass per length in both lots show high homogeneity (COV < 5%) 4 while the rest of the data show moderate homogeneity.    www.nature.com/scientificreports/  www.nature.com/scientificreports/ Mechanical and linear density properties for 10 mm diameter bars. One (1) bar from a sample of forty four (44) bars (i.e. 2.27%) from Lot 1, exhibits yield strength below the value specified by the ASTM A615/ A615M standard while in Lot 2, all the twenty seven (27) bars have the yield strength greater than 420 MPa as per the requirement of ASTM. Based on tensile strength, four bars (i.e. 9.09%) from Lot 1 exhibited tensile strength below the value specified by ASTM A615/A615M standard. But, all the bars in Lot 2 have tensile strength greater than 620 MPa as per the requirement of ASTM A615/A615M. Five bars (i.e. 11.36%) in Lot 1 exhibits elongation percentage lower than ASTM A615/A615M requirement while all bars in Lot 2 surpasses the minimum elongation percentage requirement. The mean elongation percentages in Lot 1 and Lot 2 are 13.7 and 14.4, respectively.

YS (MPa) TS (MPa) EL (%) M/L YS (MPa) TS (MPa) EL (%)
In mass per length analysis, 5 bars (i.e. 11.36%) in Lot 1 fail to meet the minimum ASTM standard for their bar size and grade. But, all the bars in Lot 2 meet the minimum requirement. The mean mass per length values in Lot 1 and Lot 2 are 0.6114 and 0.6001, respectively.
For 10 mm diameter reinforcing bar, the histogram and distribution curves are presented in Fig. 3. Lot 1 and Lot 2 show significant variability for yield and tensile strength. The mean yield strength of samples in Lot 1 and Lot 2 are 607.9 MPa and 614.7 MPa, respectively. The mean tensile strength of samples in Lot 1 and Lot 2 are 696.5 MPa and 695.9 MPa, respectively.
Even though the ratios decreased with increasing the yield strength which in turn is expected to reduce the ductility of the materials at higher yield strength, the mean TS/YS ratio of Lot 1 and Lot 2 was 1.15 and 1.13, respectively, which was below ASTM requirement. 91% of the samples in Lot 1 and 96% in Lot 2 fail to meet the TS/YS ratio of ASTM requirement. Figure 4 shows the linear regression line plot of TS/YS to YS for both lots. Mechanical strength variability of aggregate results. Figure 9 and Table 4 (1,152), 95% confidence i.e., 3.8415 1,28 . Hence, with 95% confidence, the reinforced bars appeared to be dissimilar. The apparent data spread contributes about 70% to the sample variability while the remaining 30% variation was caused by other factors. F-cal values of all parameters in both lots are greater than f . 05 , 95% confidence for its respective tabular values. Percent contribution to the variability of the data in Lot 2 is less than in Lot 1 in terms of YS, TS and elongation percentages.

Conclusion
This paper presented the results of a statistical analysis of all the relevant reinforcing steel properties of interest in Ethiopian structural construction. Over 300 data sets grouped in to two lots based on timeline of test were considered. The considered data sets include reinforcing steel bar sizes ranging from 8 to 16 mm that are widely used in different structural works in Ethiopia. Two lots that are representative of two separate test periods were compared one another based on mechanical strength and linear density property results. The comparison of these values in both lots showed that there was slight quality decline based on timeline of the tests. Aggregate strength values of YS and TS exhibited a decrease from 593.1 MPa in Lot 1 to 572.5 MPa in Lot 2 and from 701.1 MPa in Lot 1 to 673.8 MPa in Lot 2, respectively. Moreover, the results from the investigation showed that most of the samples in both lots have yield strength, tensile strength, elongation percentage and mass per length values that surpass the recommended requirements by ASTM. The result also showed that few samples had tensile to yield strength ratio that surpasses the recommended value by ASTM. The ANOVA analyses show that the data for YS, TS and TS/YS are dissimilar. In general, this class of steels used in the samples can be used for general structural applications but will not be acceptable in seismic-prone regions due to poor post elastic behavior. Material composition, source of the steel, corrosion and their effect on monotonic and fatigue loading behaviors of ribbed reinforcing Grade 60 steel bars should be studied further in the future. www.nature.com/scientificreports/